The Gamecube has several amazing titles not replicated on Wii.
Skies of Arcadia
Eternal Darkness
Prince of Persia Trilogy
Viewtiful Joe 1 and 2
Metal Gear Solid
Pikmin 1 and 2
Soul Calibur 2
Star Fox
Beyond Good and Evil
Baten Kaitos

They also still have
An extra Metroid
An extra Zelda
Original versions of RE4, Animal Crossing etc.

The Wii
More and better Mario
Wii Fit
Wii Sports
Mad World
Mursama
No More Heroes
Boom Blox
World of Goo
Okami
De Blob
Little King Story

Verdict Gamecube until after Sin and Punishment 2, Mario 2, Zelda Wii, and Metroid Other S release.

As much as I loved my little purple cube, I think I have to give it to the Wii already. I'm really enjoying Nintendo's games more this generation. That alone puts the Wii over the GameCube for me. Up to this point in time, I have enjoyed third party titles less on the Wii, but there is still a lot I have yet to play. That has plenty of time to change.

An the Wii has:

- Fire Emblem: Radiant Dawn

- Resident Evil: Umbrella Chronicles / Darkside Chronicles

- Endless Ocean 2

- Fragile Dreams

- Silent Hill: Shattered Memories

- No More Heroes 2

- Lego Star Wars

- Super Paper Mario

- Metroid Prime 3

etc. etc.

And more things to come (like Tales of Graces, Xenoblade, Epic Mickey, Other M, Galaxy 2, The Last Story)

But even yet the Wii has by far the better line-up than the gamecube. I think at the end of 2010 the Wii line up is even better than the whole PS3/Xbox360 Line-Up combined.

Much as i liked the Gamecube i think the Wii just about takes it for me. Have had more multiplayer fun (just about) on the Wii plus by the end of the gen i am sure there will be even more Wii goodness to elevate it even further past it. I think the Wii just seems a bit newer, fresher than the GC plus it has a more rounded selection of games. Not taking anything away from the GC mind, it was a very enjoyable console to play.

A lot of those Gamecube games you listed are primarily games for other systems: 
Skies of Arcadia = A Dreamcast game
Prince of Persia Trilogy = PS2 trilogy
Viewtiful Joe 1 and 2 = Brought to PS2 because they flopped on Gamecube
Pikmin 1 and 2 = Wii version of this game
Soul Calibur 2 = Bad sequel to Soul Calibur, was on PS2 and Xbox, and Soul Calibur 3 was better.
Beyond Good and Evil = PS2 game

They are simply multi platform games if you are going to degrade those games then you have to discredit every single Wii port that came from the Cube Ps2 or Xbox.

That means no more Okami, Resident Evil 4, Pikmin, Twilight Princess, Bully etc. 

The Wii has had lots of good games but the truly great games have been few and far between.

Great Gamecube games Windwaker, Smash Bros, Eternal Darkness, Mario Sunshine, Skies of Arcadia, Metroid 1 and 2, Resident Evil 4, Prince of Persia just the first one. Time Splitters 2, Beyond Good and Evil, Rouge Squadron, Twilight Princess and Pikmin series. 15 Total

The Wii has Prime 3, Mario Galaxy, New Super Mario Bros, Twilight Princess, Smash Bros, RE4 Wii, Okami, Rock Band and Mad World that is a total of 9. Mario Galaxy 2, Other M, Sin and Punishment 2, Zelda Wii, and Epic Mickey will likely make the list as well.

The Wii might have more good games but the truly great games still belong to the Cube.

However, you want a winner then pick the Wii because you can also play great Wii, N64, SNES, NES and other great games on it and the Cube cannot do that.. 

I think our definitions of great games vastly differ. Aside from Skies of Arcadia; which I played years before on Dreamcast, I don't find any of those games even appealing, leave alone great. Games that I love on Wii include:
Muramasa: The Demon Blade 
New Super Mario Brothers
Mario Galaxy
Endless Ocean
Final Fantasy 4 AY 
Wii Fit (Plus) 
Wii Sports
Wii Sports Resort
Rune Factory Frontier 
Little King's Story
Monster Hunter Tri
Wario Ware: Smooth Moves 
Mario Kart Wii

Gamecube has a total of 1, and Wii has a total of 13 by my count.

Dragon Quest X is probably the game I have been anticipating the most of any console game since Ocarina of Time or Final Fantasy 8; that one is on Wii as far as I know.

Woo, civil war. How about we wait until the Wii's corpse is cold before deciding which is best?

There is a lot of missing games in both lists.

@jumpin soul calibur 3 was better than 2???? are you mad???? 3 was the most unbalanced game in the entire series. Oh and 2 was going to b GC exclusive but then they put it on the other two, guess which version was the best??? the WII doesnt even have a proper SC game (legends doesnt count)